Baseball Basics

Baseball was the first major sport to embrace analytics. The game lends itself to recording data. The game has a small number of possible states, possible outcomes at any given moment.

One could do a term project on the development of analytics in sports, from Bill James, to Moneyball, to the present statcast era.

Rules Overview

For those unfamiliar with the game.

• Nine players per side (with substitutions available)
• Nine innings per game. Each inning has two halves.
• In each half inning one team bats, the other plays the field.
• The basic unit of action in baseball is the pitch:
  • the pitcher pitches a ball over home plate to be received by the catcher.
  • the batter tries to hit the pitch into play.
  • If the ball is hit into play, the batter tries to advance to 1st base (or beyond!).
• Possible outcomes of any one pitch:
  • ball
  • hit by pitch
  • swinging strike
  • called strike
  • foul ball
  • hit into play
  • 
• The hitting team scores a run when a player advances around the bases to return to home plate.
• The team with the most runs after 9 innings wins. (No ties, so ‘extra’ innings if necessary.)
• The scoreboard:

Team	1	2	3	4	5	6	7	8	9	R	H	E
visitor	0	1	2	0	0	1	0	0	0	4	13	1
home	2	1	0	0	3	0	1	1	x	8	9	0

• The 9 defensive positions of the fielding team:

source: whatisbaseball.com/wp-content/uploads/2019/04/Diagram-of-BB.png

• The basic outcome unit is the plate appearance (PA).

• Possible outcomes of a plate appearance

  • hit by pitch (HBP)
  • home run (HR)
  • single (1B)
  • double (2B)
  • triple (3B)
  • sacrifice fly (SF)
  • sacrifice hit (SH)
  • field out
  • ground into double play (GDP)
  • triple play (GTP)
  • error (E)
  • walk (BB) (after 4th ball)
  • strike out (K or SO) (after 3rd strike)
  • catcher interference (CI) (a replay subject to random youtube ad)

• Some base running plays

  • stolen base (SB)
  • caught stealing (CS)
  • advance on a ground out or fly out

Possible states

Baseball has a small number (24) of possible game states at the start of each plate appearance:

outs	3rd base	2nd base	1st base
0	0	0	0
0	0	0	1
0	0	1	0
0	0	1	1
0	1	0	0
0	1	0	1
0	1	1	0
0	1	1	1
1	0	0	0
1	0	0	1
1	0	1	0
1	0	1	1
1	1	0	0
1	1	0	1
1	1	1	0
1	1	1	1
2	0	0	0
2	0	0	1
2	0	1	0
2	0	1	1
2	1	0	0
2	1	0	1
2	1	1	0
2	1	1	1

A quick history of keeping statistics

• basic box score

Historically important statistics

Batting

• Hits (H)
• Home runs (HR)
• Runs batted in (RBI)
• Batting average (AVG). Batting average is defined as the ratio H/AB, where
  • H = hits, defined as the sum of singles, doubles, triples, and home runs; and
  • AB is ‘at bats’, defined as \[\text{AB = PA - (BB + HBP + SF + SH + CI)}\]

The hard to achieve hitting triple crown

Other important offensive stats, historically:

• Runs scored (R)
• Stolen bases (SB)
• Slugging percentage (SLG), \[ SLG = \frac{H + 2B + 2*3B + 3*HR}{AB}\]

Pitching - Wins (W) - Strikeouts (K) - Earned Run Average (ERA), which is defined as \[ERA = \frac{ER}{IP}*9,\] where ER represents the number of earned runs allowed by the pitcher, and IP represents the number of innings pitched. - WHIP (walks + hits per inning pitched) \[WHIP = \frac{BB + H}{IP}\]

• These statistics were (are?) of central importance in evaluating the greatness of players (MVP awards and admission to the Hall of Fame).
• But are these statistics the best measure of player performance and, more importantly, team performance?

Advanced statistics

• advanced statistics